Question 128
Let triangle $ABC$ be inscribed in a circle $\omega$, and let $M$ be the midpoint of arc $AB$ that does not contain point $C$. Let the tangent to $\omega$ at point $B$ intersect line $AC$ at point $P$. Let line $PM$ intersect $\omega$ again at point $G$. The tangent to $\omega$ at point $G$ intersects line $BC$ at point $Q$. Let lines $AB$ and $CG$ intersect at point $K$. If points $P, Q, K$, and $C$ lie on a common circle, prove that lines $KQ$ and $GB$ are parallel.
(Khulan Tumenbayar)
(Khulan Tumenbayar)